Question: Suppose that six of the 15 school buses in a particular school district have developed a slight defect since their last inspection (the steering wheel shakes when braking). Five buses are to be selected for thorough inspection. Let X denote the number of buses among the five that are inspected that have the defect.
(a) The random variable X is (choose one)
(i) binomial
(ii) hypergeometric
(iii) negative binomial
(iv) Poisson.
(b) Give the sample space and formula for the PMF of X.
(c) Use R commands to find P(2 ≤ X ≤ 4).
(d) Give the expected value and variance of X.